Question

where F is the magnitude of the gravitational attraction on either body, m1 and m2 are the masses of the bodies, r is the distance between them, and G is the gravitational constant. In SI units, the units of force are kg⋅m/s2, the units of mass are kg, and the units of distance are m. For this equation to have consistent units, the units of G must be which of the following?

Answer 1

Force = G · m₁ · m₂ / r²

In all SI units . . .

[ newton ] = [ G ] · [kg] · [kg] / [meter²]

But 'newton' is kg-m / s²
So the formula says

[ kg-m / s² ] = [ G ] · [kg] · [kg] / [meter²]

Divide each side
by kg² : kg-m / s²-kg² = [ G ] / meter²

Multiply each side
by meter² : kg-m-m² / s²-kg² = G

Cancel 'kg' from
top and bottom: m-m² / s²-kg = G

Clean it up: [ G ] = m³ / kg - s² <==

Check:
Look up "Gravitational constant" on-line:
Gravitational constant = 6.67408 × 10-11 m³ kg⁻¹ s⁻² <== yay !